Schultz was known as a point producer in junior hockey, but became an 'enforcer' in his first year of pro hockey with Salem of the EHL, prior to joining the Philadelphia Flyers, where he would become famous.

Schultz earned the nickname "The Hammer" for his aggressive style of hockey. He was one of the most notable enforcers on the Philadelphia Flyers' infamous "Broad Street Bullies." After winning two Stanley Cups with the Flyers (1973–74 and 1974–75), "The Hammer" drifted through several teams (Pittsburgh Penguins, Los Angeles Kings and Buffalo Sabres) in search of a permanent position. When GMs tried to find some "muscle" for their fledgling clubs, they thought of him.

Schultz could be more than an enforcer; he scored 20 goals for Philadelphia in 1973–74. He also scored the series-clinching goal in overtime in the first round of the 1974 Stanley Cup playoffs against the Atlanta Flames.

After injuring his wrist in a fight, Schultz once put boxing wraps on his hands for protection. As things usually went, Dave had several fights in ensuing games, while wearing the wraps. However, soon after, enforcers in both the National Hockey League and World Hockey Association started wearing similar hand protection. This was not to protect an already injured hand/wrist, but to prevent themselves from injury in a fight. Soon after this trick became popular, both the WHA and NHL passed what became known as the "Schultz Rule" — thus banning the boxing wraps' temporary involvement in professional ice hockey.